University of Vienna

About: University of Vienna is a education organization based out in Vienna, Austria. It is known for research contribution in the topics: Population & Context (language use). The organization has 44686 authors who have published 95840 publications receiving 2907492 citations.

Ordinary Differential Equations and Dynamical Systems

Abstract: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Supercompilers for parallel and vector computers

Abstract: Table of Contents * Supercomputer and Supercompilers * Supercomputer Architectures * Scalar Analysis * Data Dependence * Standard Transformations * Vectorization * Parallelization * Supercompilers and their Environments * Appendices

Universal and confident phosphorylation site localization using phosphoRS.

Abstract: An algorithm for the assignment of phosphorylation sites in peptides is described. The program uses tandem mass spectrometry data in conjunction with the respective peptide sequences to calculate site probabilities for all potential phosphorylation sites. Tandem mass spectra from synthetic phosphopeptides were used for optimization of the scoring parameters employing all commonly used fragmentation techniques. Calculation of probabilities was adapted to the different fragmentation methods and to the maximum mass deviation of the analysis. The software includes a novel approach to peak extraction, required for matching experimental data to the theoretical values of all isoforms, by defining individual peak depths for the different regions of the tandem mass spectrum. Mixtures of synthetic phosphopeptides were used to validate the program by calculation of its false localization rate versus site probability cutoff characteristic. Notably, the empirical obtained precision was higher than indicated by the applied probability cutoff. In addition, the performance of the algorithm was compared to existing approaches to site localization such as Ascore. In order to assess the practical applicability of the algorithm to large data sets, phosphopeptides from a biological sample were analyzed, localizing more than 3000 nonredundant phosphorylation sites. Finally, the results obtained for the different fragmentation methods and localization tools were compared and discussed.

Synchronization between prefrontal and posterior association cortex during human working memory

Abstract: We measured coherence between the electroencephalogram at different scalp sites while human subjects performed delayed response tasks. The tasks required the retention of either verbalizable strings of characters or abstract line drawings. In both types of tasks, a significant enhancement in coherence in the θ range (4–7 Hz) was found between prefrontal and posterior electrodes during 4-s retention intervals. During 6-s perception intervals, far fewer increases in θ coherence were found. Also in other frequency bands, coherence increased; however, the patterns of enhancement made a relevance for working memory processes seem unlikely. Our results suggest that working memory involves synchronization between prefrontal and posterior association cortex by phase-locked, low frequency (4–7 Hz) brain activity.